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人気のある微分積分 >

(x^3cos(x))^'

解

(x^{3} cos (x))^{^{'}}

解

3 x^{2} cos (x) - x^{3} sin (x)

解答ステップ

(x^{3} cos (x))^{'}

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = cos (x)

= (x^{3})^{^{'}} cos (x) + (cos (x))^{^{'}} x^{3}

(x^{3})^{'} = 3 x^{2}

(cos (x))^{'} = - sin (x)

= 3 x^{2} cos (x) + (- sin (x)) x^{3}

簡素化

= 3 x^{2} cos (x) - x^{3} sin (x)

グラフ

人気の例

integral of 1/(16x^4-8x^2+1)

\int \frac{1}{16 x ^{4} - 8 x ^{2} + 1} d x

sum from n=0 to infinity of (4n)/(8n+5)

n = 0 \sum \infty \frac{4 n}{8 n + 5}

integral from 1 to 2 of (ln(x))/(x^3)

\int_{1}^{2} \frac{ln ( x )}{x ^{3}} d x

integral of 1/((\frac{1){e^x}+1)}

\int \frac{1}{( \frac{1}{e ^{x}} + 1 )} d x

normal y=x^2-5x,(5,0)

n or ma l y = x^{2} - 5 x, (5, 0)